Chiral Lagrangians with $\Delta (1232)$ to one loop

Abstract

We construct the Lorentz-invariant chiral Lagrangians up to the order $\mathcal{O}(p^4)$ by including $\Delta (1232)$ as an explicit degree of freedom. A full one-loop investigation on processes involving $\Delta (1232)$ can be performed with them. For the $\pi \Delta \Delta$ Lagrangian, one obtains 38 independent terms at the order $\mathcal{O}(p^3)$ and 318 independent terms at the order $\mathcal{O}(p^4)$. For the $\pi N\Delta$ Lagrangian, we get 33 independent terms at the order $\mathcal{O}(p^3)$ and 218 independent terms at the order $\mathcal{O}(p^4)$. The heavy baryon projection is also briefly discussed.

23 pages,8 tables. Less terms are found with more constraints. Version accepted by PRD

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Cited by in corpus (8)

• Weak pion production off the nucleon in covariant chiral perturbation theory
• Chiral Lagrangians for mesons with a single heavy quark
• Light-quark mass dependence of the nucleon axial charge and pion-nucleon scattering phenomenology
• Chiral Lagrangians with decuplet baryons to one loop
• Relations for low-energy coupling constants in baryon chiral perturbation theory derived from the chiral quark model
• Chiral Lagrangians for spin-$\frac{1}{2}$ and spin-$\frac{3}{2}$ doubly charmed baryons
• Chiral Lagrangians for singly heavy baryons to $\mathcal{O}(p^4)$ order
• Axial-vector nucleon-to-delta transition form factors using the complex-mass renormalization scheme